Boundary of the Horseshoe Locus for the Hénon Family

DOI10.1137/18M1174684zbMath1408.37059arXiv1803.09381OpenAlexW2795327467MaRDI QIDQ4686625

Zin Arai, Yutaka Ishii, Hiroki Takahasi

Publication date: 4 October 2018

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.09381

zbMATH Keywords

Hénon maphorseshoe locustangency

Mathematics Subject Classification ID

Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Bifurcations connected with nontransversal intersection in dynamical systems (37G25) Dynamical systems over complex numbers (37F99)

Related Items

Dynamics of polynomial diffeomorphisms of \(\mathbb {C}^2\): combinatorial and topological aspects, On parameter loci of the Hénon family, Iterative roots of two-dimensional mappings

Cites Work

• Shift automorphisms in the Henon mapping
• Non-expansive Hénon maps
• On parameter loci of the Hénon family
• Equilibrium Measures at Temperature Zero for Hénon-Like Maps at the First Bifurcation
• Equilibrium measures for the Hénon map at the first bifurcation
• Thermodynamic formalism for a family of non-uniformly hyperbolic horseshoes and the unstable Jacobian
• Real polynomial diffeomorphisms with maximal entropy: II. Small Jacobian
• Dynamical properties of plane polynomial automorphisms
• Rigorous Computations of Homoclinic Tangencies